Internal problem ID [11943]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 7, Systems of linear differential equations. Section 7.1. Exercises page
277
Problem number: 16.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-2 t -t^{2}\\ y^{\prime }\left (t \right )&=-3 x \left (t \right )+y \left (t \right )+2 t +2 t^{2} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
dsolve([2*diff(x(t),t)+diff(y(t),t)-x(t)-y(t)=-2*t,diff(x(t),t)+diff(y(t),t)+x(t)-y(t)=t^2],singsol=all)
\begin{align*} x \left (t \right ) &= \frac {t^{2}}{2}+\frac {3 t}{2}+\frac {3}{4}+c_{2} {\mathrm e}^{2 t} \\ y \left (t \right ) &= \frac {15}{4}-3 c_{2} {\mathrm e}^{2 t}+\frac {3 t}{2}-\frac {t^{2}}{2}+c_{1} {\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 67
DSolve[{2*x'[t]+y'[t]-x[t]-y[t]==-2*t,x'[t]+y'[t]+x[t]-y[t]==t^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} \left (2 t^2+6 t+4 c_1 e^{2 t}+3\right ) \\ y(t)\to -\frac {t^2}{2}+\frac {3 t}{2}-3 c_1 e^{2 t}+(3 c_1+c_2) e^t+\frac {15}{4} \\ \end{align*}